Numerical Efficiency of the Conjugate Gradient Algorithm - Sequential Implementation

In the paper we report on a second stage of our efforts towards a library design for the solution of very large set of linear equations arising from the finite difference approximation of elliptic partial differential equations (PDE). Particularly a family of Krylov subspace iterative based methods (in the paper exemplified by the archetypical Krylov space method Conjugate Gradient method) are considered. The first part of the paper describes in details implementation of iterative algorithms for solution of the Poisson equation which formulation has been extended to the three-dimensional. The second part of the paper is focused on the performance measurement of the most time-consuming computational kernels of iterative techniques executing basic linear algebra operations with sparse matrices. The validation of prepared codes as well as their computational efficiency have been examined by solution a set of test problems on two different computers.